Related papers: Are Percolation Transitions always Sharpened by Ma…
This article studies stochastic relative phase stability, i.e., stochastic phase-cohesiveness, of discrete-time phase-coupled oscillators. Stochastic phase-cohesiveness in two types of networks is studied. First, we consider oscillators…
We present an exact mathematical framework able to describe site-percolation transitions in real multiplex networks. Specifically, we consider the average percolation diagram valid over an infinite number of random configurations where…
It was recently found that cascading failures can cause the abrupt breakdown of a system of interdependent networks. Using the percolation method developed for single clustered networks by Newman [Phys. Rev. Lett. {\bf 103}, 058701 (2009)],…
Motivated by the importance of geometric information in real systems, a new model for long-range correlated percolation in link-adding networks is proposed with the connecting probability decaying with a power-law of the distance on the…
The robustness of complex networks against node failure and malicious attack has been of interest for decades, while most of the research has focused on random attack or hub-targeted attack. In many real-world scenarios, however, attacks…
In this paper we consider a transformation which converts uncorrelated networks to correlated ones(here by correlation we mean that coordination numbers of two neighbors are not independent). We show that this transformation, which converts…
Networks of weakly coupled oscillators had a profound impact on our understanding of complex systems. Studies on model reconstruction from data have shown prevalent contributions from hypernetworks with triplet and higher interactions among…
We investigate the propagation of perturbations in Boolean networks by evaluating the Derrida plot and modifications of it. We show that even small Random Boolean Networks agree well with the predictions of the annealed approximation, but…
Aspects of cell metabolism are modeled by ordinary differential equations describing the change of intracellular chemical concentrations. There is a correspondence between this dynamical system and a complex network. As in the classic…
The event graph representation of temporal networks suggests that the connectivity of temporal structures can be mapped to a directed percolation problem. However, similar to percolation theory on static networks, this mapping is valid…
Many real-world systems can be modeled as interconnected multilayer networks, namely a set of networks interacting with each other. Here we present a perturbative approach to study the properties of a general class of interconnected…
Controlled experimental studies of percolation are challenging due to difficulties in tuning site connectivity, isolating local interactions, and mitigating finite-size effects. In this work, we experimentally investigate percolation with a…
Neural operators have achieved strong performance in learning solution operators of partial differential equations (PDEs), but their inherently continuous representations struggle to capture discontinuities and sharp transitions. Existing…
We study the sensitivity of directed complex networks to the addition and pruning of edges and vertices and introduce the susceptibility, which quantifies this sensitivity. We show that topologically different parts of a directed network…
Bootstrap percolation is a well-known model to study the spreading of rumors, new products or innovations on social networks. The empirical studies show that community structure is ubiquitous among various social networks. Thus, studying…
We study living neural networks by measuring the neurons' response to a global electrical stimulation. Neural connectivity is lowered by reducing the synaptic strength, chemically blocking neurotransmitter receptors. We use a…
The observed architecture of ecological and socio-economic networks differs significantly from that of random networks. From a network science standpoint, non-random structural patterns observed in real networks call for an explanation of…
Co-evolutionary adaptive mechanisms are not only ubiquitous in nature, but also beneficial for the functioning of a variety of systems. We here consider an adaptive network of oscillators with a stochastic, fitness-based, rule of…
Rigidity Percolation is studied analytically on randomly bonded networks with two types of nodes, respectively with coordination numbers $z_1$ and $z_2$, and with $g_1$ and $g_2$ degrees of freedom each. For certain cases that model…
The power of networks manifests itself in a highly non-linear amplification of a number of effects, and their weakness - in propagation of cascading failures. The potential systemic risk effects can be either exacerbated or mitigated,…